Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+4y &= 6 \\ 5x+5y &= 5\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = -5y+5$ Divide both sides by $5$ to isolate $x$ $x = {-y + 1}$ Substitute this expression for $x$ in the first equation. $-({-y + 1}) + 4y = 6$ $y - 1 + 4y = 6$ Simplify by combining terms, then solve for $y$ $5y - 1 = 6$ $5y = 7$ $y = \dfrac{7}{5}$ Substitute $\dfrac{7}{5}$ for $y$ in the top equation. $-x+4( \dfrac{7}{5}) = 6$ $-x+\dfrac{28}{5} = 6$ $-x = \dfrac{2}{5}$ $x = -\dfrac{2}{5}$ The solution is $\enspace x = -\dfrac{2}{5}, \enspace y = \dfrac{7}{5}$.